Tssp-2024-25
Содержание
What-about
Course whitepaper
Course goals
侍には目標がなく道しかない [Samurai niwa mokuhyō ga naku michi shikanai]
A samurai has no goal, only a path.
Telegram chat
Grading
Stochastic Processes = 0.35 Halloween Exam + 0.40 Ded Moroz Exam + 0.25 Home Assignments
Time Series Analysis = 0.30 Mimoza Exam + 0.45 Sakura Exam + 0.25 Home Assignments
Home assignments
Home assignments have equal weights. You have 4 honey weeks for the whole year.
Exams
Midterm alpha: Tuesday, 5 November at 18:10.
Samurai diary
Lecture slides and class notes
2024-09-02, lecture 1:
2024-09-09, lecture 2:
2024-09-16, lecture 3: Markov chain: communicating classes. Transient states. Recurrent states.
2024-09-24, lecture 4: Idea of generating function: describe collection of objects as a function and extract information from function. How to extract E(X), E(X^2), E(XY), P(X=3) from a function that generates outcomes. Formal definition of probability generating function and moment generating function.
2024-10-30, lecture 5:
2024-10-07, lecture 6:
2024-10-14, lecture 7: Sigma-algebra is a way to model information, formal definition. Calculating sigma-algebra generated by two events or by discrete random variable. Filtration is a growing sequence of sigma-algebras. Formal definition of conditional expected value with respect to sigma-algebra.
2024-10-21, lecture 8:
Classes
Class video recordings
Maria Kirillova notes
2024-09-06, class 1: First step analysis, 1.1 from StoPro.
More on first step analysis: section 2.7.2 in In2Pro
2024-09-13, class 2: First step analysis, 1.4 from StoPro.
2024-09-20, class 3: Classification of states in Markov chain, communicating classes, 3.1ab from StoPro.
2024-09-27, class 4: Generating functions: standard normal distribution, chi-squared with 1 degree of freedom.
2024-10-04, class 5: Calculating probability limit using LLN. Intuition behind probability limit: unique forecast that is "arbitrary good" for almost all X_n. Probability limit of max and min. Probability limit is a random variable. Probability limit of iid sequence does not exist.
2024-10-11, class 6: Two more limits (in probability and in L2), conditional expected value in uniform case, conditional expected value with joint density.
2024-10-18, class 7: Calculation of sigma-algebra generated by random variable. Calculation of expected value wrt to sigma-algebra.
2024-11-01, class 8: Checking that a process is a martingale, 9.1abcd, 9.9 from StoPro.
2024-11-08, class 9: Poisson point process
Sources of Wisdom
StoPro: Problems in Stochastic Processes
In2Pro: Blitstein, Hwang, Introduction to probability.
MarkovTex: Representing Markov Chains in Latex.
Mchains Cambridge lectures on Markov chains.
Takis: Takis Konstantinopulos, One hundred solved exercises on Markov chains.
Past course iterations: 2023-2024, 2022-2023, 2021-2022, 2020-2021.
Convergence modes review from Cornell university
Convergence modes: Saravan Vijayakumaran, convergence modes with examples
